HD VoIP in the Asterisk world involves selecting the G722 codec for VoIP calls.G722 is known as a wideband codec as opposed to g711 which is narrowband.

The nice thing about it is that it does not require any more bandwidth than G711. Both require 64kbit/s each way for a 2-way conversation.

The difference is that G722 employs compression combined with a higher sample rate to obtain a practical acoustic bandwidth of 50 Hz-7000 Hz as opposed to G711 which has a practical acoustic bandwidth of 200-3000 Hz.

The difference in voice quality is quite noticeable. Instead of sounding like you are talking into a tin can it now sounds like the other person is in the same room.
You can hear more subtle nuances in the person’s voice and certain letters/syllables that are hard to distinguish on regular calls become much easier.

If one endpoint is using G722 and the other is using G711, the endpoint using G722 will hear better sound quality from the other end but the G711 end will not notice much if any difference.

Transcoding overhead between G722 and g711 is minimal. Roughly equivalent to half the transcoding overhead between G711 and GSM. G.722 patents have expired, so it is freely available.